Find a vector that has the same direction as −6, 4 but has length 6.

Answer 1

Hello,

This means that: y/x=-4/6=-2/3 (same direction) and sqrt(x²+y²)=6 (magnitude).

We have two equations and two unknowns…

y=-(2/3)x from the first equation. Substitute this into the second:

Sqrt(x²+(-2/3)x²)=6

Sqrt((13/9)x²)=6

… (algebra)

x=±18/sqrt(13)

Let “x” be NEGATIVE since the x component is negative in the problem (Quadrant II).

Substitute back in to find y.

-(2/3)*(-18/sqrt(13))=12sqrt(13)/13.

So the solution is:

<-18sqrt(13)/13,12sqrt(13)/13>

I hope this helps!

Answer 2

6< -6/√52, 4/√52>